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Observed and modeled patterns of covariability between low-level cloudiness

and the structure of the trade wind layer

Article in Journal of Advances in Modeling Earth Systems · October 2015

DOI: 10.1002/2015MS000483

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JAMES, VOL. ???, XXXX, DOI:10.1002/,

Observed and modeled patterns of co-variability1

between low-level cloudiness and the structure of the2

trade-wind layer3

Louise Nuijens,1

Brian Medeiros,2

Irina Sandu,3

Maike Ahlgrimm3

Key points.4

• KEY POINT #1: models reveal unrealistic variability in cloudiness at short time scales5

• KEY POINT #2: models overestimate variations in cloudiness near the LCL with RH and6

temperature lapse rates7

• KEY POINT #3: models underestimate relationships that matter for cloudiness near the8

inversion on long time scales9

Corresponding author: L. Nuijens, Max Planck Institute for Meteorology, Bundesstrasse 53,

20146 Hamburg, Germany. ([email protected])

1Max Planck Institute for Meteorology,

D R A F T October 7, 2015, 1:25pm D R A F T

X - 2NUIJENS ET AL.: CO-VARIABILITY CLOUDINESS AND TRADE-WIND LAYER STRUCTURE

Abstract. We present patterns of co-variability between low-level cloudi-10

ness and the trade-wind boundary layer structure using long-term measure-11

ments at a site representative of dynamical regimes with moderate subsidence12

or weak ascent. We compare these with ECMWF’s Integrated Forecast Sys-13

tem and ten CMIP5 models. By using single-timestep output at a single lo-14

cation, we find that models can produce a fairly realistic trade-wind layer15

structure in long-term means, but with unrealistic variability at shorter time16

scales.17

The unrealistic variability in modeled cloudiness near the lifting conden-18

sation level (LCL) is due to stronger than observed relationships with mixed-19

layer relative humidity (RH) and temperature stratification at the mixed-20

layer top. Those relationships are weak in observations, or even of opposite21

Bundesstrasse 53, D-20146, Hamburg,

Germany.

2National Center for Atmospheric

Research, PO BOX 3000, Boulder, CO,

USA, 80307

3European Centre for Medium-Range

Weather Forecasts, Shinfield Park, Reading

RG29AX, United Kingdom


NUIJENS ET AL.: CO-VARIABILITY CLOUDINESS AND TRADE-WIND LAYER STRUCTURE X - 3

sign, which can be explained by a negative feedback of convection on cloudi-22

ness.23

Cloudiness near cumulus tops at the trade-wind inversion instead varies24

more pronouncedly in observations on monthly time scales, whereby larger25

cloudiness relates to larger surface winds and stronger trade-wind inversions.26

However, these parameters appear to be a prerequisite, rather than strong27

controlling factors on cloudiness, because they do not explain sub-monthly28

variations in cloudiness. Models underestimate the strength of these relation-29

ships and diverge in particular in their responses to large-scale vertical mo-30

tion. No model stands out by reproducing the observed behaviour in all re-31

spects.32

These findings suggest that climate models do not realistically represent33

the physical processes that underlie the coupling between trade-wind clouds34

and their environments in present-day climate, which is relevant for how we35

interpret modeled cloud feedbacks.36


X - 4 NUIJENS ET AL.: CO-VARIABILITY CLOUDINESS AND TRADE-WIND LAYER STRUCTURE

1. Introduction

Steady winds and abundant fields of shallow trade-wind cumuli over the open ocean37

characterize the trades and give these regions in the subtropics an important role in38

climate. Surface evaporation under strong winds supplies the moisture that is needed for39

trade-wind cumuli to form. Trade-wind cumuli themselves transport moisture away from40

the surface throughout the lower troposphere, thereby setting its vertical structure and41

further increasing surface evaporation. By reflecting solar radiation trade-wind cumuli42

also increase the albedo, providing a modest (but persistent) cooling influence.43

Although the trades are a relatively steady weather regime compared to other regions on44

Earth, the strength and direction of the trade-winds, sea surface temperatures and large-45

scale vertical motion do show marked variability on daily, seasonal and inter-annual time46

scales [Brueck et al., 2015]. There is no doubt that changes in any of these parameters can47

induce changes in trade-wind clouds and the structure of the lower atmosphere, but their48

combined effects and resulting patterns of co-variability are not sufficiently understood.49

Our objective is to expose relationships between trade-wind cloudiness and the structure50

of the trade-wind layer in observations and to provide insight into the overall sensitivity51

of trade-wind cloudiness to changes in the large-scale flow. Furthermore, we evaluate52

whether patterns of co-variability between cloudiness and the trade-wind layer structure53

in global models are consistent with those observed.54

In previous work we showed that the amount of variance in trade-wind cloudiness in55

global (climate) models diverges from observations. Specifically, a common bias of climate56

models is to vary the amount of cloud near the lifting condensation level (LCL) more than57



is observed [Nuijens et al., 2015]. Several models also produce a trade-wind boundary58

layer that is too shallow, which leads to an underestimation of the variance in cloud59

amount in the cloud layer and near the trade-wind inversion. This study follows up on60

our previous work by relating the variability in cloudiness to variability in the structure61

of humidity, temperature, winds and large-scale vertical motion. We will expose the ways62

in which models produce clouds, which may differ from nature, thereby providing insight63

into whether models capture the physical processes that underlie the coupling between64

clouds and their environment.65

If global models can reproduce patterns of co-variability in our current climate, we may66

have more confidence in their responses to future forcing scenarios, even though present-67

day variability is not necessarily a good proxy for future climate change. Climate models68

currently have different responses to future forcing scenarios due, in part, to different69

changes in trade-wind cloudiness. In some models trade-wind cloudiness decreases as70

climate warms, which amplifies the warming and leads to a high climate sensitivity. In71

other models trade-wind cloudiness increases, which leads to a low climate sensitivity72

[Bony and Dufresne, 2005; Medeiros and Stevens , 2011; Vial et al., 2013]. Brient et al.,73

submitted to Climate Dynamics, show that the profile of cloud fraction in the trades74

in present-day climate is a good predictor for whether a climate model has a high or a75

low climate sensitivity. A high climate sensitivity model tends to have large values of76

cloudiness only near the LCL, much like stratocumulus, whereas a low climate sensitivity77

model distributes cloudiness more evenly across a deeper trade-wind layer. Sherwood et al.78

[2014] further propose a link between the different responses of models and the different79

ways models mix moisture across the lower troposphere. For instance, they suggest that80



when a model efficiently transports moisture away from the surface it tends to have a high81

climate sensitivity. Such a model could efficiently dry the lower atmosphere as climate82

warms, which would lead to a reduction of low-level cloudiness.83

Observations are crucial for evaluating whether changes in cloudiness with vertical mois-84

ture mixing in climate models are realistic, but over the open ocean measurements are85

mostly limited to space-borne remote sensing. However, observing the humidity and tem-86

perature structure in the lower atmosphere is challenging from space, especially in cloudy87

conditions. Space-borne instruments often lack the resolution to reveal vertical gradients88

that might be crucial for cloudiness. Shallow cumuli also have dimensions typically much89

smaller than satellite footprints. Furthermore, polar orbiting satellites view the same90

location on Earth only every couple of days, so that variability can only be studied on91

time scales of a month and longer. For climate models a similar (practical) issue is true:92

conventional model output includes only monthly averages, which may hide variability on93

shorter time scales that are critical to the mean behavior of clouds.94

Ongoing approaches strategically address the need for evaluating global models against95

observations by making use of permanent ground-based meteorological sites that measure96

clouds and the structure of the atmosphere at a high temporal and vertical resolution. For97

instance, the Cloud-Associated Parameterizations Testbed (CAPT) applies weather fore-98

cast techniques to climate models to evaluate model parameterizations at measurement99

sites of the Atmospheric Radiation Measurement Program (ARM) of the U.S. Department100

of Energy [Phillips et al., 2004]. Similarly, the KNMI Parameterization testbed (KPT)101

runs Large-Eddy Simulation (LES) and Single-Column Models (SCM) at ARM and Eu-102

ropean CloudNet sites [Neggers et al., 2012]. Because these approaches sample and model103



clouds across a wide range of conditions they have successfully led to the identification104

of systematic biases in modeled physics, such as a compensating error between cloud105

structure and radiative transfer due to cloud overlap assumptions [Neggers and Siebesma,106

2013]. A few years ago, the Cloud Feedback Model Intercomparison Project (CFMIP) also107

initiated the so-called cfSites output, which includes single-timestep output from many108

climate models at 120 strategically located sites [Webb et al., 2015].109

Unfortunately, the number of such sites is limited in the trades. To fill this gap in110

observational data, the Max-Planck Institute for Meteorology, jointly with the Caribbean111

Institute for Meteorology and Hydrology, installed a long-term measurement site in 2010:112

the Barbados Cloud Observatory (BCO, 13◦N 59◦W). The Island of Barbados is the113

most eastward located island in the West Indies facing the North Atlantic ocean. The114

airmasses and clouds advected to the site are therefore little influenced by land or the115

island itself (Stevens et al., submitted to BAMS). The location experiences moderate116

large-scale subsidence during boreal winter and weak ascent during boreal summer [Brueck117

et al., 2015], which are exactly those regimes in which climate models differ the most in118

their structure of low-level clouds and response to warming. Under these large-scale119

conditions, the majority of trade-wind clouds found at Barbados are located well below120

3 km, although deep convection and cirrus form an important contribution to high-level121

cloud cover and therefore to total cloud cover (Medeiros and Nuijens, in preparation for122

PNAS).123

At Barbados, cloudy layers near the LCL at 700 m and near the trade-wind inversion124

at 1.5 - 2.5 km contribute most to low-level cloud cover [Nuijens et al., 2014]. Cloud125

amount near the LCL is of interest because it is the dominant contribution to cloud cover126



and is relatively invariant in time. Moreover, cloud amount near the LCL at Barbados is127

remarkably similar to the cloud amount near the LCL over all subtropical oceans. This is128

illustrated in Figure 1, which is adapted from earlier papers [Nuijens et al., 2014; Medeiros129

et al., 2010]. The black line represents the distribution of cloud layer bases as viewed by130

a laser ceilometer with a footprint of ∼500 m deployed at the BCO between 2010 and131

2014. The blue solid line represents the distribution of cloud layer bases as viewed by132

CALIOP (the lidar aboard the CALIPSO satellite), when it overpassed a region close133

to the BCO between 2010 and 2014. CALIOP has a comparable footprint of ∼333 m.134

The instruments give a sense of the height levels at which cloud layers are frequent and135

contribute to low-level cloud cover. Both instruments show that at Barbados cloud layers136

are most frequent near the LCL, although CALIOP underestimates the frequency. Likely137

this underestimation is caused by the attenuation of the lidar beam due to the longer path138

travelled and due to overlying high cloud. Notwithstanding, the frequency of CALIOP139

detecting a cloud layer near the LCL is remarkably similar for the BCO area and the140

subtropical oceans in the Northern Hemisphere and Southern Hemisphere, where the141

latter are shown by solid respectively dashed light blue profiles.142

Cloud layers further aloft, near the trade-wind inversion, are of interest for another rea-143

son: The cloud amount at this level is much more variable in time and in space [Nuijens144

et al., 2014]. At Barbados the most important contribution to cloud amount near the145

inversion is from stratiform layers near cumulus tops, followed by slanted tops of cumuli146

and short-lived patches of decaying cloud [Nuijens et al., 2014]. The stratiform layers de-147

velop when trade-wind cumuli grow into a cloud layer that is capped by a relatively strong148

inversion [Stevens et al., 2001; Lock , 2009], often typified as the intermediate or transi-149



tion regime: between regions of stratocumulus underneath strong inversions at eastern150

ocean boundaries and regions of trade-wind cumuli in deeper boundary layers at western151

boundaries. Apparently this regime can be observed even this far west over the Atlantic.152

At the BCO, both the ceilometer at the BCO and CALIOP show a similar frequency of153

occurrence of cloud layers at the inversion. Over all NH and SH subtropical oceans, be-154

cause larger areas of the intermediate and stratocumulus regimes are included, CALIOP155

detects a larger frequency of cloud near the inversion.156

In the remainder of this manuscript, we will focus on these two height levels (the LCL157

and near the trade-wind inversion) to explain variability (or lack thereof) in cloudiness158

near the BCO. We perform similar exercises for the models, which include ten climate159

models that have supplied the cfSites single-timestep output for Barbados (or a nearby160

location), as well as the Integrated Forecast System (IFS) from the European Centre for161

Medium-Range Weather Forecasts (ECMWF), which has been run in a climate-model-162

like (year-long) integration mode. We will draw out similarities and differences from the163

observations, as well as how models diverge. Finally, we discuss how these results relate164

to climate change studies that hint at the importance of the shallowness of the cloud layer165

and vertical moisture mixing.166

2. Data, model output and methods

We use ground-based radar, lidar and ceilometer data from the BCO combined with167

the ERA-Interim reanalysis product to derive relationships between cloudiness and the168

thermodynamic and kinetic structure of the trade-wind layer. We do the same for model169

output, which includes single-timestep output from long integrations with the Integrated170

Forecast System (IFS) from the European Centre for Medium-Range Weather Forecasts171



(ECMWF) model and single-timestep output from nine CMIP5 models. The following172

sections 2.1-2.4 describe the data and model output in more detail. We explain how we173

compare cloudiness in the models with that in the observations in section 2.5.174

2.1. Barbados Cloud Observatory data

The BCO is located on an eastward promontory of the island of Barbados (13.15◦N,175

59.4◦W) and has a suite of instrumentation similar to the Department of Energy (DOE)176

ARM sites. The period April 2010 - April 2012 is used to derive statistics. Cloud cover177

(CC) is defined as the fraction of time (here either daily or monthly) that a ceilometer178

with a temporal resolution of 30 s measures a cloud base height overhead. We distinguish179

between the contribution of cloud at heights near the LCL to cloud cover (hereafter180

referred to as CCLCL) and the contribution of cloud at heights further aloft (CCALOFT)181

by separating cloud bases that are detected below or above 1 km. Because the ceilometer182

measured almost continuously, these data provide some of our most important statistics.183

When rainfall is strong enough, the ceilometer cannot detect a cloud base height. This184

is true for 60% of the rain events, which cover 7% of the data [Nuijens et al., 2014]. Hence,185

for 4.2% of the observed profiles we cannot meaningfully separate the two components186

of CCLCL and CCALOFT. For these 4.2% we also cannot assess whether hydrometeors187

measured by the radar represent rain that falls through a detectable cloud base or rain188

that falls through the cloud layer out of slanted clouds. In our derivation of CC (as well189

as of cloud fraction (CF), see next paragraph) we exclude these 4.2% of data. This means190

that we underestimate total cloudiness in the observations by excluding heavily raining191

cloud, a bias we are willing to accept given our focus on qualitative behavior. Because192


NUIJENS ET AL.: CO-VARIABILITY CLOUDINESS AND TRADE-WIND LAYER STRUCTUREX - 11

these cases comprise only 4.2% of the record, they also do not substantially bias our193

results.194

Cloud fraction (CF) profiles are derived from the Ka band (36 GHz) Doppler radar195

(KATRIN) when in a vertically pointing mode from January 2011 to mid May 2011,196

October 2011 and from January 2012 to March 2012. Data include profiles every 10 s197

with a resolution of 30 m from 300 m up to 15 km. Radar returns with an equivalent198

radar reflectivity Ze larger than -40 dBZ are defined as true hydrometeor returns. We199

exclude profiles for which no ceilometer cloud base height is available (strong rainfall, see200

above) and mask all returns below the lowest detected cloud base height that are likely201

drizzle.202

Humidity and temperature profiles are measured with a multi-channel Raman lidar,203

from April 1, 2011 - April 1, 2012. By measuring backscattered energy at the shifted204

Raman frequency, in the UV spectral range at 355 nm, the concentration of water vapor205

is derived. The pure rotational Raman spectra (PRRS) technique is used to derive air206

temperature [Serikov and Bobrovnikov , 2010]. The profiles of humidity and temperature207

are only available during nighttime when there is no interference of background solar208

light, between 0 - 8 UTC (20h-04h local time). The lidar hatch also closes when the MRR209

detects rain-rates > 0.05 mm h−1 at any height below 3 km. The raw data is averaged210

into 2 minute profiles for water vapor and 1 hourly profiles for temperature, available at211

a 60 m resolution up to 15 km.212

For more details on the sensitivity of CC and CF to our subjective thresholds of defining213

cloud we refer the reader to Nuijens et al. [2014].214



2.2. ERA-Interim

The ERA-Interim reanalysis product is used for daily and monthly profiles of the zonal215

and meridional wind components (u, v), and the vertical velocity (ω). It is based on the216

Cy31r2 version of the IFS [Simmons et al., 2007]. The horizontal resolution (N128) of the217

quasi-regular gaussian grid is approximately 0.7◦ at 10◦N. The vertical resolution is 61218

model levels, with a pressure difference that increases from 4 hPa in the lowest levels to219

40 hPa at a pressure of 440 hPa. The profiles are averaged over a 5◦x5◦ region upstream220

of Barbados.221

2.3. ECMWF IFS

Long climate-model-like integrations are produced with the ECMWF IFS (ECMWF-222

LI). Unlike short integrations, which start every day from a state that is corrected by data223

assimilation procedures, these climate-model-like integrations are forecasts initialized only224

once a year, on the 1st of August. They are performed at a T255 spectral resolution which225

corresponds roughly to a grid box of (75 x75) km2 at the Equator. The output is therefore226

comparable to the CMIP5 model output. We performed four of these long integrations227

for the years 2009 - 2012 with an IFS version that was operational between June 2013 and228

November 2013 (IFS Cycle 38r2). Single-timestep (30 minute) output was extracted from229

all these runs for a single grid point near Barbados, centered at 13.68◦N, 59.06◦W. The230

integrations are performed on 91 vertical levels, of which only the output for the lowest231

31 levels is used, reaching from 10 m to 7600 m with a spacing of 20 m at level 1 and232

500 m at level 31. We found that qualitatively, the cloud fields in these long integrations233

are similar, or even closer to observations, than output from short (24 hour) integrations234

[Nuijens et al., 2015].235



2.4. cfSites output from CMIP5 models

Single-timestep output of nine climate models for a single grid point near Barbados is236

available through the cfSites initiative from the Cloud Feedback Model Intercomparison237

Project (CFMIP) [Webb et al., 2015]. The output is produced from Atmospheric Model238

Intercomparison Project (AMIP) runs from 1976 - 2006, constrained by observed sea239

surface temperatures and sea ice. Although thirty years of data is available, five years240

(2001-2006) suffices for most of our analysis. The CMIP5 models and their acronyms are241

listed in Table 2. For all models the location closest to Barbados at which cfSites output242

is produced is the BOMEX location (15◦N 56.5◦W). For the MPIM-E62 and MPIM-E63243

models we also produced output at a grid point near the BCO (13.2◦N 59.4◦W). Although244

the BOMEX location experiences fewer periods with mean rising motion, we believe it245

largely suffices for exploring models’ behavior of trade-wind cloudiness. For most models246

these grid points correspond to an area of about (100 x 100) km2.247

The MPIM-E62 and MPIM-E63 output is not obtained from the CMIP5 archive, but we248

have rerun the model with the newer ECHAM versions 6.2 and 6.3, wherein errors in the249

way statistics are accumulated have been fixed. For most models single-timestep output250

means 30 minute output, except for the BCC model, which comes every 20 minutes. Two251

out of three timesteps of the BCC model have zero cloud fractions everywhere, which252

seems an issue with the way the output has been produced. Therefore we only use every253

third time step. We do the same for the NCAR-C4 model, which has zero cloud fractions254

every other time step.255

2.5. Cloud fraction and cloud cover in observations and models



Cloudiness in models and in observations are inherently different. An often used tech-256

nique to overcome these differences and compare models with observations is to use for-257

ward operators or cloud simulators implemented in models. These simulate how cloud258

predicted by the model would be measured by a given instrument. However, our analysis259

focuses on qualitative rather than quantitative behavior of cloudiness. For instance, we260

study the shape of the cloud fraction profile or the variability of cloud fraction in time.261

To identify differences in such qualitative aspects between models and observations it is262

not necessary to apply a forward operating technique. For a similar reason we also do263

not interpolate the observations onto a coarser vertical grid that is representative of the264

models’ grids.265

We do account for the difference in temporal or horizontal resolution: the observations266

have a footprint of just a few tens of meters, whereas a single model grid point is equivalent267

to an area of about (100 x 100) km2. The BCO time series is first averaged to a period268

that represents the time needed for an air mass to travel across a 100 km distance. Wind269

speeds are observed to be about 7 ms−1 on average, which equals four hour of BCO270

measurements. In all figures and analysis where time scales are mentioned the averaging271

of the BCO data is implicit, unless we explicitly state otherwise.272

CF refers to the amount of cloud that is present at a given height or pressure level,273

whereas CC is the total amount of cloud projected onto the surface, only from cloud that274

is present at heights below 5 km (≈ 550 hPa). As discussed in the introduction, we focus275

on cloudiness at two levels: near the LCL and near the tops of the deepest cumuli, just276

below the trade-wind inversion (see also Nuijens et al. [2014] and the continuing discussion277

on in section 3). We define CFLCL in observations and in models as the cloud amount at278



the LCL, which we take as the level at which the RH profile maximizes. A list of LCL’s279

for the observations and models is given in Table 2. Furthermore, we define CFALOFT as280

the average cloud fraction between 850 and 800 hPa.281

In the observations CF is intermittent due to frequent downtimes of the cloud radar282

(section 2.1). For certain analyses we therefore use the more continuous time series of CC283

instead, which we separate into two contributions: from cloud bases detected below 1 km284

(CCLCL) and above 1 km (CCALOFT), which qualitatively capture variations in CFLCL and285

CFALOFT [Nuijens et al., 2014]. Because we contrast environments in which cloudiness is286

abundant or not, focusing on cloudiness more qualitatively than quantitatively, we freely287

use observed CCLCL or CCALOFT alongside modeled CFLCL and CFALOFT. Because many288

models just have one or two vertical levels between 950 and 900 hPa, corresponding to289

the mean LCL and 1 km, their CCLCL would principally be equal or very close to CFLCL.290

When we use observed CC instead of observed CF we indicate this in the figure caption.291

For simplicity we just refer to CF throughout the text, but flagged with a star (CF*LCL,292

CF*ALOFT).293

3. Vertical structure of clouds and their environment

This section provides a general overview of the most important features of the trade-294

wind layer including the cloud profile. First, we describe the observed and modeled295

long-term mean profiles for periods of moderate subsidence and of weak ascent. Second,296

we discuss the variability in cloudiness and the structure of the trade-wind layer on shorter297

daily time scales.298



3.1. Long-term means

In the dry season from December through May Barbados experiences large-scale flow299

that is typical of the fair-weather trade-wind regime. The region is in the subsiding branch300

of the Hadley circulation and strong winds with a northerly component advect relatively301

colder and drier air from higher latitudes towards Barbados. As the InterTropical Con-302

vergence Zone (ITCZ) migrates northward in the wet season from June - November, the303

region experiences moderate rising motion instead (ω < 0). Sea surface temperatures304

are about 2 K higher and smaller pressure gradients between the subtropics and Equator305

drive weaker winds [Brueck et al., 2015]. Deep convective events and even an occasional306

hurricane are not uncommon.307

Despite these differences in large-scale flow and free tropospheric temperature and hu-308

midity, the dry and the wet season have similar cloud structures. Mean profiles of cloud309

fraction (CF), the relative humidity (RH), virtual potential temperature (θv) and the310

frequency distribution of inversion levels (pinv) are shown in Figure 2. The black line cor-311

responds to Jan - Mar (the dry season) and the grey line to Sep - Nov (the wet season).312

The lower atmosphere is both drier and colder during the dry season. Cloud base height313

(LCL) is located near 925 hPa, which coincides with a maximum in RH. The layer near314

the LCL at the top of the well-mixed layer is often called the transition layer, because315

RH more sharply decreases than in the (upper) cloud layer. In the dry season, the LCL is316

somewhat higher, the transition layer is more pronounced and a separation between the317

cloud layer and the inversion layer is distinct. However, even during the dry season the318

location of the inversion (pinv, which is the pressure level of the maximum θv gradient at319

p> 600 hPa) can range anywhere between 825 to 600 hPa on a daily basis. Such vari-320



ability smooths the inversion structure when profiles are averaged; individual profiles are321

likely to have much more pronounced inversions than the mean.322

In both seasons CF throughout the cloud layer is about 0.08, but there are some im-323

portant differences. The wet season gets more deep convection, which increases CF and324

RH above 800 hPa, but reduces CF near 825 hPa due to less stratiform cloud layers near325

cumulus tops [Nuijens et al., 2014]. Also note that there is a hint of more frequent stable326

layers near 950 hPa from the distribution of pinv in Figure 2, which could be a result from327

compensating downward motion from deep convection, which stabilizes the environment,328

or from evaporation of rain below cloud base.329

The smaller CF near 825 hPa in the wet season is responsible for a modest reduction330

in low-level cloud cover (CC) [Nuijens et al., 2014]. This modest seasonality in CC is331

not just apparent in the BCO measurements, but also in data from active and passive332

satellite sensors for a region upstream of Barbados (Medeiros and Nuijens (in preparation333

for PNAS), [Brueck et al., 2015] .334

Most models have a maximum in CF near the top of the well-mixed layer with values335

less than 0.3 (Figure 2, remaining panels). They thus capture the basic feature of trade-336

wind cloudiness: a partially cloudy layer with clouds that are produced most frequently337

near the LCL. Many models place the trade-wind inversion near and above 825 hPa and338

therefore produce cloud layer depths similar to observations. Moreover, several models339

reproduce the layered structure of the trade-wind layer, including the increase in RH in340

the well-mixed layer up to the LCL and a decrease in RH in the cloud layer. Some models341

even show a hint of a transition layer in their RH profiles and distribution of pinv.342



Many models are systematically too dry in the upper part of the cloud layer (850-825343

hPa), but most of them predict the warming and moistening towards the wet season.344

The associated changes in the CF profile at levels below 850 hPa are small, consistent345

with the observations. Models thus reproduce the robustness of the trade-wind layer.346

Nevertheless, no model stands out as performing particularly well at capturing the finer347

details, including the difference in LCL between the seasons, the invariance of CF near348

the LCL and most importantly, the decrease in CF near 825 hPa.349

These points will be discussed in more detail when we relate cloudiness to the structure350

of the trade-wind layer (section 4.2). First, we will take a closer look at how models vary351

the structure of cloud and humidity on shorter time scales.352

3.2. Short-term variability

How a model arrives at its mean CF profile can be very different from the observations.353

In the observations individual days experience clouds that are fairly evenly distributed354

over a layer from the LCL to the mean inversion height, whereas in the models the vertical355

distribution of clouds can differ substantially from one day to the next.356

The shape of the CF profile can be measured by a parameter γ = CFLCL / (CFLCL +357

CFALOFT), which represents how bottom-heavy (large γ) or top-heavy (small γ) the CF358

profile is (Brient et al., submitted to Climate Dynamics). Distributions of γ from daily359

CF profiles are shown in black in Figure 3 a (dry season) and d (wet season). Values for360

γ are always less than 0.6, which implies that CF is distributed across the cloud layer and361

tends to be emphasized near the top of the cloud layer especially in the dry season.362

Compared to observations, models differ greatly in their distributions of γ. Several363

models shift between very bottom-heavy (γ > 0.9) and top-heavy profiles (γ < 0.1). This364



behaviour of γ is related to frequent occurrences of CFLCL = 0 or CFALOFT = 0 (square365

markers on the left outset of Figure 3b-c, e-f). However, in the observations there are366

very few days on which CF at either level is completely absent. This is even more true for367

CCLCL (in black solid lines) because it represents a cloud amount integrated over many368

observed heights within one model layer.369

In observations the total variance in CFALOFT is about twice that of CFLCL (see Table370

2, whose values were previously shown in Nuijens et al. [2015]). Hence, variability in371

cloudiness near the inversion is the dominant contributor to variability in low-level CC.372

In contrast, six out of nine models have in total more variance in CFLCL than in CFALOFT373

(Table 2), which is caused by their frequent dissipation of CF near the LCL.374

Periods with zero CFLCL can in some models last for days or weeks at a time [Nuijens375

et al., 2015], which suggests that the behaviour is not random. In the following sections,376

we analyze if such behaviour can be linked to the modeled trade-wind structure and377

large-scale flow.378

4. Patterns of co-variability of cloud and environment

The results presented in previous sections hint that patterns of co-variability between379

cloudiness and the environment are systematically different in the models compared to ob-380

servations. For CFLCL and CFALOFT respectively, section 4.1 and 4.2 reveal the anomalous381

profiles of RH, absolute humidity q, potential temperature θ, vertical velocity ω and the382

wind components u, v for months with large and small CF - in observations and models.383

The anomalies are taken with respect to a yearly running mean centered on each month.384

Furthermore, we perform regressions between CF and parameters that one may call385

large-scale predictors, which have been found important for explaining variations in cloudi-386



ness in previous studies [Brueck et al., 2015]. These parameters include the RH averaged387

over the well-mixed layer (〈RH〉ML), the vertical difference in RH between 850 hPa and388

the LCL (∆CLRH = RH850-RHLCL) and the vertical difference in RH across the inversion389

layer (∆ILRH = RH700-RH850). Furthermore, the potential temperature lapse rate across390

the transition layer or mixed-layer top is considered, dθ/dzTL, which for the observations391

is derived between 1000 and 900 hPa and for the models between one model level above392

and below the LCL (which are not always separated by 100 hPa, hence we take the actual393

gradient here instead). The free tropospheric θ lapse rate is also considered, whereby ∆ILθ394

is determined between 750 and 600 hPa. Lastly, the vertical velocity at 825 hPa (ω825)395

and the near-surface wind speed UL0 are included.396

4.1. Cloudiness near the LCL

4.1.1. Observed versus modeled seasonal patterns397

In observations the differences in CF*LCL from one month to the next are generally398

modest, but there are a few notable differences. Months with larger CF*LCL (thick black399

lines, Figure 4) have a drier well-mixed layer, a relatively moist cumulus layer and a very400

dry and warm layer near and above the inversion between 825 hPa and 600 hPa compared401

to months with smaller CF*LCL (thin black lines). The dry and warm air between 825-402

600 hPa is likely associated with the intrusion of Saharan Dry Air layers, which occurs403

throughout late Spring and early summer [Carlson and Prospero, 1972].404

Relatively cold cloud layers over warm well-mixed layers destabilize the cloud layer to405

convection and triggers abundant cloudiness within the first 1.5 km above the LCL. The406

cloudiest months also have stronger winds, with a more pronounced northerly component,407

which is consistent with the air masses being relatively cold (in θ) and dry (in q). A408



separation in the vertical wind component, ω, is only visible above 825 hPa, which suggests409

that months with large-scale subsidence generally have larger CF*LCL, but that ω is not410

a decisive factor.411

We have already seen that models tend to have more variance in CFLCL than is observed,412

with frequent occurrences of CFLCL = 0 (Table 2 and Figure 3c). Therefore it might not413

come as a surprise that models co-vary CFLCL with the environment in a number of414

ways. As the anomaly profiles for a subset of models illustrate, increases in humidity415

and temperature, winds and subsidence can either increase or decrease CFLCL (Figure 4).416

Some models are close to the observed behaviour (BCC, NCAR-C4), but have weaker and417

more southerly winds at times of large cloudiness instead. Other models show very little418

separation in profiles (MPIM-E62) or produce more CFLCL during months with mean419

rising motion (ω < 0) that have a moister and warmer trade-wind layer (ECMWF-LI,420

MOHC and NCAR-C5).421

In the following section we discuss the relationships of cloudiness with the environment422

in more detail by looking at daily and monthly time scales. To simplify the discussion we423

perform single and multi-variate regressions of cloudiness with the large-scale predictors424

defined above.425

426

4.1.2. Predictors of cloudiness427

To facilitate the comparison between models and observations, which differ in their428

magnitudes and in their variances of CF, a standardized regression is used whereby the429

regression coefficients are scaled by the ratio of the standard deviation of a parameter430

to the standard deviation of CF. Table 3 lists the parameter that explains most of the431



variance, using a single regression for each parameter, as well as using a multi-variate432

regression, which basically removes the effect of covarying parameters that may strengthen433

or weaken individual relationships. The single regression coefficients are also plotted in434

Figure 5 for the different time scales. The regressions for different time scales are created435

by first removing the long-term mean before performing the regression. For instance,436

monthly means are subtracted from daily means and yearly means are subtracted from437

monthly means.438

The observed regressions for CF∗LCL turn out to be overall small and negligible for439

most parameters - including RH. Altogether the selected set of parameters explains 24%440

of the observed total variance on daily time scales and 56% of the observed total variance441

on monthly time scales. UL0 and dθ/dzTL are the parameters that best explain monthly442

variations in CF*LCL (30% each).443

All models run counter to the observations by producing excessive CFLCL when the well-444

mixed layer is relatively humid and topped by a more stable transition layer. 〈RH〉ML and445

dθ/dzTL explain at least half of the variance in monthly CFLCL (last column, Table 3).446

In addition, the models lack the observed relationships between CFLCL and UL0, or that447

relationship has the opposite sign.448

The time series in Figure 6 illustrate the relationship between CFLCL and RH in obser-449

vations (top two panels) and a few models for which the regression coefficients between450

CFLCL and 〈RH〉ML are larger than 0.7 at monthly time scales. The observations show that451

CCLCL has day-to-day variations, but stays close to 20% on longer time scales. Although452

co-variations between daily RHLCL and CFLCL can be observed, CFLCL does not exhibit453

the multi-day (i.e., synoptic) fluctuations that RH does. The models’ single-timestep be-454



havior shows that their variances in CFLCL are much larger than observed, which in some455

models (e.g., MPIM-E62) are tightly linked to RH variations (cf. Figure 5).456

Behind the behavior we derive from the models appears to linger well-established re-457

lationships between low-level cloudiness, relative humidity, the stability of the lower at-458

mosphere and the large-scale vertical velocity, which in climatologies separate patterns of459

cloudiness along latitude and inspired cloud parameterizations decades ago. For example,460

many climate models use a diagnostic cloud scheme whereby CF is some function of the461

RH, assuming that condensation on sub-grid scales is related to a larger scale synoptic462

regime that makes an imprint on the mean relative humidity [Slingo, 1980; Sundqvist463

et al., 1989; Qu et al., 2014]. Larger cloud amounts, such as belonging to stratocumulus464

decks, have also been linked to regions with enhanced lower tropospheric stability [Klein465

and Hartmann, 1993]. Therefore, vertical temperature gradients, as well as vertical veloc-466

ity ω, have likely made their way into parameterizations of cloudiness. However, because467

these parameters do not reflect the dominant mechanisms that control CF on shorter time468

scales, they might lead to overly strong dependencies.469

In the following section we explain why relationships between CF∗LCL and the large-scale470

environment are small on short time scales in the observations. We hypothesize about the471

underlying processes that lead to the observed relationships with UL0 and dθ/dzTL and dis-472

cuss reasons for the somewhat counterintuitive result that 〈RH〉ML plays only a minor role.473

474

4.1.3. Constraints on cloudiness near the LCL in nature475

In the observations there is little evidence for strong controlling factors on CF∗LCL.476

One of the explanations for this is that CF∗LCL,when averaged over a day or longer has477



relatively little variance (compared to CF∗ALOFT, see also Table 2). Nuijens et al. [2015]478

show that 60% of the total variance in CF∗LCL is contained on time scales less than a479

day. This suggests that processes that have relatively short time scales are important in480

regulating cloudiness, which in turn are relatively insensitive to changes in the large-scale481

flow, such as large-scale subsidence or large-scale relative humidity. For instance, larger482

CF∗LCL is found during months with lower 〈RH〉ML (Figure 5), which shows that RH is483

not a decisive factor.484

Using the high-resolution nighttime humidity measurements at the BCO, which provide485

a humidity profile every 2 minutes, we find that the location of the mixed-layer top (η)486

with respect to the LCL of air parcels near the surface is decisive for cloudiness near487

the LCL on short time scales. Humidity anomalies for 15 minute periods during which488

CF∗LCL is large or small (compared to the nighttime mean) are most pronounced near489

700 m, but less so towards the surface (Figure 7). Because the layer below η tends to490

be well-mixed, we expect q to be relatively constant with height, which implies that the491

signal in q at 700 m merely reflects an increase of η.492

This finding is not surprising. Going back to early work by Malkus [1958] it has been493

recognized that for cumulus clouds to form, buoyant air parcels need to ascend through494

a stable layer, the transition layer, which is similar to a layer of convective inhibition in495

studies of deep convection. The transition layer is marked by a small decrease in absolute496

humidity and increase in temperature, which reflects the penetrative nature of the dry497

convection in the sub-cloud layer: the overshooting and downward mixing of relatively498

dry and warm air. This is illustrated in part 1 of Figure 8, adapted from Neggers et al.499

[2006]. In this illustration we also indicate that the LCL is not just one height level, but500



at a range of levels, because buoyant parcels ascend from different levels in the well-mixed501

layer that have different humidity and temperature values. An increase in η with respect502

to the mean LCL, or vice-versa, a decrease of the mean LCL, will increase the fraction of503

parcels that reach saturation.504

A handful of studies in the past decade have built simple models of cumulus convection

around the idea that the location of η with respect to the LCL, as well as the difference in

humidity and temperature across the mixed-layer top, are regulated by cumulus convection

itself (sometimes called the cumulus-valve mechanism) [Albrecht et al., 1979; Neggers et al.,

2006; Stevens , 2006; Fletcher and Bretherton, 2010]. These ideas are helpful to understand

observed modulations of η on relatively short time scales and provide an explanation for

why CF∗LCL has little variance on longer time scales. In such models the mass budget of

the well-mixed layer is written as:

dη

dt= E −M + wη (1)

where E is the rate at which cloud layer air is entrained into the sub-cloud layer (E > 0,

and ≈ 1 cms−1). wη is the large-scale vertical velocity, which is < 0 downward and ≈ 0.5

cms−1. Finally, M is the mass removed from the layer by convection. M can be written

as the product of wc, the vertical velocity in the positively buoyant cores of clouds, and

of ac, the cloud core fraction:

M = wc ac (2)

A typical core fraction ac is on the order of a few percent (0.01-0.05), which may be505

understood from the balance ac ≈ E−wηwc

and assuming equilibrium (dηdt

= 0). For updrafts506

with wc ≈ 1 ms−1 this leads to M ≈1 cms−1. Let us imagine a scenario by which the507



well-mixed layer is perturbed and q increases by δq, which lowers the LCL and leads to508

a ten-fold increase in ac (#1 and 2, Figure 8). Following Equation 2, M consequently509

increases by an order of magnitude to 10 cms−1, which has the potential to lower η by a510

100 m in only 1000 s. The net effect is to lower η, bringing it closer to the mean LCL511

again, which constitutes the negative feedback. At the same time, the amount of dry air512

that is pushed down by convective downdrafts helps increase the stability by increasing513

∆TLq. Both processes lead to a reduction in the fraction of air parcels that saturate, which514

reduces M and brings the well-mixed layer to a new equilibrium state (# 3 in Figure 8).515

Note that a difference exists between the cloud core fraction ac and the actual CF. CF is516

determined by all cloudy air parcels, including those that are negatively buoyant, whereas517

ac only includes the fraction of positively buoyant parcels. LES indicates that values for518

CF are a factor 2 to 10 larger than ac [Siebesma et al., 2003; VanZanten et al., 2011]. What519

might control differences between the two warrants further investigation, but at first order520

we may assume that the two are proportional and postulate that because convection acts521

to keep η and the LCL close to one another [Albrecht et al., 1979], variations in CF∗LCL522

are also limited.523

Using this framework, it can be understood that the RH in the well-mixed layer can524

help regulate the LCL and thus CF∗LCL on shorter time scales. However, such local525

variations are poorly encapsulated in the RH averaged over a day or longer. Why we526

do not see a stronger relationship with RH on even shorter time scales (not shown) is527

somewhat surprising, and in contrast with studies that have successfully linked humidity528

and temperature variations to cloudiness, most notably the work by [Tompkins , 2002] on529

statistical (PDF) cloud schemes. The temporal resolution of the measurements may play530



a role: although the updrafts and downdrafts are likely resolved, the larger humidity in531

the core of the updraft may not be. Furthermore, temperature fluctuations that matter532

to cloudiness on short time scales are not resolved.533

There appear to be mechanisms that may change CF∗LCL on monthly time scales:534

namely, dθ/dzTL has a negative relationship with CF∗LCL and UL0 has a positive relation-535

ship with CF∗LCL. These relationships may be understood from Equation 1 by noting that536

different equilibria (dηdt

= 0) are possible. Larger dθ/dzTL may correspond to a smaller en-537

trainment rate E and hence a smaller η, which would correspond to smaller ac. As for the538

wind speed, which has appeared as an important factor in numerous studies [Klein, 1997;539

Brueck et al., 2015], but generally receives less attention compared to thermodynamic540

arguments: an increase in UL0 linearly increases the surface buoyancy flux Fb,s. Energeti-541

cally, the effect of larger Fb,s is to increase the depth of the well-mixed layer η (through an542

increase in E): that deeper layer allows the vertical gradient of the buoyancy flux, which543

determines the local heating rate, to remain unchanged, in order to balance an unchanged544

radiative cooling rate [Nuijens and Stevens , 2012]. Thermodynamically, the effect of a545

larger wind speed is to lower the LCL. This is due to a decrease in the Bowen ratio and546

an increase in RH, due to a larger increase in the surface latent heat flux compared to547

the surface sensible flux, the latter being limited by the entrainment of relatively warm548

air [Albrecht et al., 1979; Betts and Ridgway , 1989]. The increase in η through energetic549

constraints and the decrease in LCL through thermodynamic constraints would increase550

cloudiness. Other possibilities through which stronger winds may impact cloudiness are551

when they are accompanied by increased convergence, either locally, or when the ITCZ is552

located at higher latitudes in boreal summer (assuming that winds vanish at the ITCZ).553



Increased convergence would raise η by making wh less negative. Stronger winds may also554

imply a larger wind shear, which would increase the projected cloud cover, although wind555

shear appeared a less important controlling factor than wind speed itself [Brueck et al.,556

2015]. We also note that the anomaly profiles of u and v (Figure 4) do not suggest a557

strong role for shear. LES modeling studies would be necessary to better understand all558

these interactions.559

560

4.2. Cloudiness aloft

4.2.1. Observed and modeled seasonal patterns561

Large values of CF*ALOFT occur when numerous shallow cumuli near the LCL are ac-562

companied by larger and deeper cumuli with stratiform layers near their tops [Nuijens563

et al., 2014]. We have seen that stratiform cloud layers are more pronounced during the564

dry winter season (Figure 2, section 3.2). Therefore, the anomalous profiles during pe-565

riods of large CF*ALOFT versus small CF*ALOFT (Figure 9) mainly reflect the dry and566

wet seasons. Months with larger CF*ALOFT are relatively drier and colder, experience567

large-scale subsidence, larger UL0 and larger wind shear. These months also have a no-568

table trade-wind inversion between 800 - 700 hPa. Both Klein [1997], focusing on the569

stratocumulus-to-cumulus transition region, and Brueck et al. [2015], focusing on a region570

upstream of Barbados, found that low-level CC is best correlated with wind speed. Both571

studies also emphasize that the airmass history matters: air masses coming from colder,572

drier regions (under stronger subsidence) have larger lower tropospheric stability, which573

may promote low-level CC.574



That said, the deeper clouds may occur during disturbed periods much shorter than a575

month, which deviate from the mean conditions during the dry season, a point which we576

return to in the next section.577

The models in Figure 9 diverge in their patterns. Some models resemble the observa-578

tions and have larger CFALOFT in the dry season (IPSL and ECMWF-LI) when the free579

troposphere is dry and warm and mean subsidence prevails. Other models show the op-580

posite: larger CFALOFT is produced at times of mean ascent, when the inversion is weaker581

and the lower troposphere is more humid (MRI, CNRM, MOHC and NCAR-C5). During582

those months the boundary layer overall appears to be much deeper and moister than583

what is typical for the trades.584

Similar to what we did for CFLCL we next compare the regressions of CFALOFT with585

a set of predictors to discuss the most apparent relationships across time scales in the586

observations and the models.587

588

4.2.2. Predictors of cloudiness589

On a day-to-day basis CF*ALOFT varies more strongly with RH in the cloud layer (mea-590

sured by ∆CLRH, which scales mostly with RH825) and with ω825 than what we have591

seen for CF*LCL. The fraction of variance explained by the selected set of predictors is592

also larger (0.44, compared to 0.24 for CF*LCL, Table 4). The stronger covariance can593

be explained because the main source of RH in the cloud layer is convection itself, which594

transports moisture out of the mixed-layer into the free troposphere. This relationship is595

already present on time scales of minutes (Figure 7b) and explains why the daily regression596

coefficient between CF*ALOFT and ∆CLRH is relatively large at 0.5 (Figure 10).597



Days with larger CF*ALOFT also correspond to weaker subsidence or larger mean ascent,598

so that the regression coefficient with ω825 is negative on daily time scales (Figure 10).599

This hints that synoptic disturbances, such as easterly waves, can promote CF*ALOFT600

even when on average that month experiences subsiding motion. Consistent with that re-601

lationship, the regression coefficient with ∆ILRH is positive on daily time scales, reflecting602

a deepening and moistening of the cloud layer.603

Also on monthly time scales the variance in CF*ALOFT is somewhat better explained by604

the selected set of predictors than the variance in CCLCL. However, the covariance with605

∆CLRH (RH825) is less pronounced, presumably because that covariance exists locally and606

is poorly encapsulated in longer averages. Parameters that do play an important role are607

∆ILθ and UL0. What may underlie these relationships is a greater potential for stratiform608

cloud layers to form under stronger inversions when surface evaporation is large [Nuijens609

and Stevens , 2012]. However, those conditions appear to be a prerequisite rather than610

a controlling factor, because neither covary strongly with CF*ALOFT on the shorter daily611

time scales.612

The results suggest that an important factor for increasing CF*ALOFT and CC is the613

potential for trade-wind cumuli to deepen, but nevertheless maintain a limited depth so614

that the trade-wind layer structure is preserved. If the trade-wind inversion becomes less615

defined because much deeper convection transports moisture all the way through the cloud616

and inversion layers into the free troposphere, such as during the wet season (Figure 2,617

light grey line), CFALOFT will decrease.618

All models agree with the observations that days with larger ∆CLRH and weaker sub-619

sidence correspond to larger CFALOFT (Figure 10). Yet whereas such parameters become620



less important in the observations on monthly time scales or relationships between these621

parameters and CFALOFT change sign, the majority of models continue to show strong622

relationships with ∆CLRH and ω825. Models disagree on the sign of the relationship with623

ω825, which leads to opposing anomaly profiles (Figure 9). Some models produce the624

largest CFALOFT in the wet season with strongest mean ascent (MRI, CNRM), whereas625

others reproduce the observations by producing the largest CFALOFT in the dry season626

when strong inversions as well as stronger winds are present (ECMWF-LI, IPSL). Many627

models fail to reproduce the observed relationships with UL0 and ∆ILθ, although a few628

models capture at least the relationship with ∆ILθ (BCC, IPSL, NCAR-C4) or with UL0629

(ECMWF-LI).630

5. Discussion

We have identified some common biases of global (climate) models in how they vary631

trade-wind cloudiness with the environment. First, models have stronger than observed632

relationships between CFLCL and the RH in the well-mixed layer. We explained that in633

nature, variations in RH may regulate the LCL and thus be linked to cloud formation634

locally, but that these local signatures diminish over longer time scales. Furthermore,635

we explained how convection responds rapidly to perturbations in RH by ventilating the636

mixed-layer, which has a negative feedback on CFLCL (section 4.1.3). Apparently climate637

models do not represent such processes properly. Therefore, modeled CFLCL appears to638

be too sensitive to changes in RH.639

Second, models have stronger than observed relationships between CFLCL and the tem-640

perature stratification at the top of the well-mixed layer. Models produce larger CFLCL641

when the transition layer and lower cloud layer are more stratified, whereas in observations642



larger cloudiness near the LCL is found when these layers are less stratified. Observations643

do show larger CFALOFT underneath a stronger trade-wind inversion further aloft, which644

many models do not reproduce.645

The models diverge in how they distribute CF and RH across the depth of the trade-646

wind layer. While some models reduce CFLCL as the RH in the cloud layer and CFALOFT647

increase, other models keep CFLCL unchanged or even increase it.648

We illustrate these different behaviours by means of Figures 11 and 12, which combine649

the behaviours of CFLCL and CFALOFT seen in Figure 5 and 10. The panels in Figure650

11 represent how parameters differ between days with a uniform distribution of moisture651

across the cloud layer and days with a less uniform distribution of moisture, whereby the652

latter is measured by ∆CLRH. These differences, δ’s, are derived as follows: we order all653

days by ∆CLRH, from high to low values, and select the upper and lower quartiles of days.654

Because ∆CLRH is generally negative, the upper quartile corresponds to small negative655

∆CLRH (well-mixed) and the lower quartile to large negative ∆CLRH (larger gradients656

in RH throughout the cloud layer). δ ≡ φupper − φlower corresponds to the difference657

in a parameter φ between those two quartiles, whereby φupper is the average φ over the658

upper quartile or days (and similar for the lower quartile). The grey shaded box indicates659

negative δ’s.660

The range of values for δ(∆CLRH) on the x-axis (20 - 70%) illustrates that models661

have a much larger variance in RH gradients in the cloud layer than the observations662

suggest. Nevertheless, both observations and models agree that days with largest ∆CLRH663

correspond to larger CFALOFT and that the actual change in CF, which is less than 0.2, is664

modest (Figure 11a). In observations those changes are accompanied by a small increase665



in CFLCL (Figure11b). A number of models instead show a large decrease in CFLCL666

that falls into the grey shaded area. These models have the largest decreases in γ∗, which667

indicates that the models switch from bottom- to top-heavy profiles (δγ < 0, (Figure11c)),668

whereas in observations the CF profile becomes only slightly more top-heavy (remember669

also Figure 3). Because some of these models (MPIM-E62, CCCma) have large CFLCL670

to begin with, and little to no CFALOFT, these changes can be quite effective at reducing671

low-level CC overall. The same models also show that the RH in the mixed-layer decreases672

(δ〈RH〉ML < 0, Figure11d) when the distribution of RH in the cloud layer becomes more673

uniform.674

Brient et al. (submitted to Climate Dynamics) show that models that produce a bottom-675

heavy profile more effectively reduce cloudiness as climate warms and therefore have a high676

climate sensitivity. Our findings suggest that these models exhibit stronger relationships677

between CF and RH near the LCL than in observations. These models tend to shift678

cloud layers near the LCL to levels further aloft when moisture is mixed upward and the679

cumulus layer deepens, rather than sustaining cloudiness everywhere within the cumulus680

layer. The negative relationship between RH or CF near the inversion (850 hPa) and681

CF near the LCL is also apparent in a larger sample of CMIP models over all ocean682

regions that experience moderate subsidence or weak ascent (Medeiros and Nuijens, in683

preparation for PNAS).684

Sherwood et al. [2014] furthermore show that the simulated vertical moisture structure685

over tropical oceans in present-day climate separates high from low climate sensitivity686

models. They use ∆ILRH as a measure of lower tropospheric mixing and relate models687

with a small ∆ILRH to a high climate sensitivity. By diagnosing ∆ILRH only over the688



western Pacific warm pool, where mean ascent dominates, they ensure that convection689

is indeed the lead effect on moisture at those levels, rather than variations in large-scale690

descent. They then argue that those models that sustain small ∆ILRH are apparently very691

effective at mixing moisture all the way from the well-mixed layer to the free troposphere692

(700 hPa). Presumably, as this mixing increases with global mean temperature CFLCL693

disappears.694

We find that models that are effective at mixing moisture by the definition of Sherwood695

et al. [2014] are indeed those that readily dissipate clouds near the LCL in the present-696

day climate. These are the models in Figure 11 that reduce temperature and moisture697

gradients throughout the lower troposphere as they reduce CFLCL. An illustration of698

this behaviour using the MPIM-E62 model as an example is shown in Figure 12b. The699

potential temperature difference across the inversion layer decreases (δ∆ILθ <0) and so700

does the temperature stratification across the transition layer (δ∆TLθ < 0). Furthermore,701

the RH difference across the inversion layer decreases (δ∆ILRH > 0, because ∆ILRH702

becomes less negative).703

This behavior contrasts with other models, which distribute RH and CF more uniformly704

across the cloud layer, so that as CFALOFT increases, CFLCL changes little or increases by705

a small amount (MOHC, NCAR-C5, ECMWF-LI). The MOHC model is used to illustrate706

this behaviour (Figure 12c). These models tend to maintain the structure of the trade-707

wind layer, in terms of layers separated by gradients. The associated larger temperature708

stratification in the transition layer in these models (δ dθ/dzTL > 0) may provide an709

additional mechanism through which moisture is capped within the well-mixed layer,710

which sustains cloud layers there. On the other hand, these models have a much stronger711



than observed positive relationship between CFLCL and large-scale ascent (Figure 5). Of712

the models that we have analyzed here, the BCC, NCAR -C4 and MRI models have a713

low climate sensitivity in Sherwood et al. [2014]. In turn, high climate sensitivity models714

in Sherwood et al. [2014] include the MPIM-E62, IPSL, CCCma and CNRM models.715

In observations, neither a large decrease nor a large increase in CFLCL is evident when716

large-scale vertical motion or RH in the cloud layer changes. However, it would be easy to717

misjudge a model’s behavior as being more realistic, and therefore its climate sensitivity718

as more trustworthy, by means of a single process such as vertical moisture mixing. There719

is no model that stands out by reproducing observed relationships in all respects. The720

climate models that we have analysed here for instance lack either constraints on CFLCL721

due to convection, a sensitivity to wind speed and the strength of the trade-wind inversion,722

or an insensitivity to large-scale vertical velocity on longer time scales. Because changes723

in cloudiness will be a combined response to changes in a variety of factors (see also724

Bretherton et al. [2013]), many of which are connected through circulations and some of725

which are regulated by convection itself, a better understanding of the role of large-scale726

circulations versus the role of convection deserves more attention.727

6. Summary and conclusions

We evaluated global (climate) models for their ability to reproduce observed patterns of728

co-variability between the structure of the trade-wind layer, cloudiness and the thermo-729

dynamic and kinetic environment. A ground-based measurement site established on the730

Island of Barbados has provided the data required to study such variability in detail. We731

used these measurements for a period of up to four years and compared them to multi-year732

single-timestep output from models at a single site near or upstream of Barbados. The733



models include a subset of CMIP5 models and the ECMWF Integrated Forecast System;734

we ran the latter in a climate-model-like long integration mode.735

All the models exhibit the basic observed features of a trade-wind layer. Specifically,736

models produce a well-mixed layer approximately 500-1000m deep throughout which RH737

increases, peaking at cloud base at a value less than 100%. Accordingly, CF is on average738

smaller than 0.4 throughout the cloud layer. The location of the trade-wind inversion739

in both observations and models ranges from 850 hPa (≈ 2 km) to 600 hPa (≈ 4 km),740

reflecting the ability of trade-wind cumuli to reach substantial depth. As the ITCZ mi-741

grates northward in boreal summer and vertical motion at Barbados changes from mean742

descent to mean ascent, temperatures increase throughout the column and RH increases743

above the trade-wind layer. Corresponding changes in the CF profile are relatively small,744

which the majority of models reproduce.745

However, when moving away from long-term means and looking at variability instead it746

is evident that models achieve their fairly realistic climatology through rather unrealistic747

variability on shorter time scales. This raises an important question, namely whether748

models can capture potential changes in trade-wind cloudiness in a warmer climate.749

Variability in cloudiness is analyzed at two important height levels: 1) near the lifting750

condensation level (LCL) or cloud base (CFLCL), and 2) near the detrainment level (cloud751

tops) of the deepest cumuli at the trade-wind inversion (CFALOFT). CFLCL is important752

because it contributes on average two-thirds to low-level cloud cover and is relatively753

invariant when averaged over a few days or longer. Relationships between CFLCL and754

RH, or other measures of the trade-wind layer structure, are weak. We explained that755

a negative feedback of cumulus convection on CFLCL, which can be found in theoretical756



models of convection, appears present in the observations. In this negative feedback,757

cumulus convection acts like a valve on top of the well-mixed layer that removes mass758

as soon as cloud formation is abundant. This mechanisms maintains the height of the759

mixed-layer top in the vicinity of the LCL, which in turn constraints CF.760

CFALOFT on the other hand is important because it contributes most to the variance761

in low-level cloud cover. CF at this level covaries with the strength of the trade-wind762

inversion and with surface wind speed on monthly time scales, leading to larger CFALOFT763

in boreal winter, when the trade-winds are stronger and lower tropospheric stability is764

larger. However, variance in CFALOFT on shorter daily time scales is unexplained by these765

factors.766

None of the models that we analyzed stands out by reproducing the observations better767

in all respects. Almost all models overestimate the variance in CFLCL compared to the768

variance in CFALOFT on shorter (daily) timescales. The large variance in modeled CFLCL769

lies in stronger than observed relationships between CFLCL and RH in the well-mixed770

layer. Furthermore, whereas in nature modest decreases in CFLCL are observed when the771

temperature stratification in the transition layer is larger (and convection is limited), the772

models show larger CFLCL under such conditions instead.773

Most models do not indicate that the strength of the inversion and the surface wind774

speed can promote CFALOFT in boreal winter. Models diverge in how they distribute CF775

and RH vertically across the trade-wind layer and in particular in response to changes776

in large-scale vertical motion. One group of models places most cloud layers near the777

LCL in a shallow layer with large CF. Cloud layers aloft are produced when moisture is778

transported away from the surface to levels near and above the inversion. This dries the779



mixed-layer and lower part of the cloud layer at the expense of CFLCL. A very bottom-780

heavy profile (no CFALOFT) is then exchanged for a very top-heavy profile (no CFLCL).781

These models behave like the ones that Sherwood et al. [2014] refers to as models with782

a large vertical mixing potential, which effectively dry the mixed layer and cloud layer783

when climate warms. These models appear to reduce cloudiness, especially near the LCL,784

too eagerly when vertical mixing increases. Another group of models distributes RH and785

CF more uniformly across the cloud layer, so that CF near the LCL is maintained when786

moisture is mixed upwards and CF aloft increases. However, this increase is strongly787

linked to periods of mean ascent, which is unsupported by the observations.788

Modeled cloud changes in present-day climate thus appear to have a larger susceptibility789

to changes in their environment than the observations. This highlights that cloudiness in790

models is not entirely regulated by the processes that underlie variations in cloudiness in791

nature, which decreases our confidence that climate models can realistically predict the792

response of trade-wind clouds to increasing global temperatures.793

Acknowledgments. The BCO infrastructure is maintained by Ilya Serikov, Lutz794

Hirsch, Friedhelm Jansen, Bjoern Bruegmann, Monika Pfeiffer and Holger Linne, and795

without them this work would not have been possible. Many thanks go to Bjorn Stevens796

and Robert Pincus for helpful discussions on earlier versions of the manuscript. We also797

thank Rodrigo Colpo for his work on the CMIP5 output, Sebastian Massart for his help798

with retrieving IFS data, Andrew Gettelman for retrieving the BOMEX cfSites output799

for CAM4 and CAM5 and Jobst Musse for compiling the CALIOP data in Figure 1. Two800

reviewers greatly helped to improve the readability of the manuscript. LN appreciates801

the hospitality of NCAR and ECMWF during part of this work. BM acknowledges sup-802



port by the Regional and Global Climate Modeling Program of the U.S. Department of803

Energy’s Office of Science, Cooperative Agreement DE-FC02-97ER62402. NCAR is spon-804

sored by the National Science Foundation. The BCO data, the ECMWF long integra-805

tions and the cfSites output for MPIM-E62, CAM4, CAM5 are available upon contacting806

the first author. The cfSites output for the remaining models can be downloaded from:807

http://cmip-pcmdi.llnl.gov/cmip5/data portal.html.808

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ground-based at BCOspace-borne near BCO

15 - 30 NH15 - 30 SH

inve

rsio

nLC

L

Figure 1. Lidar observations of the vertical distribution of cloud layer bases in the trades as

viewed from ground (in black) respectively from space (in blue). The distribution is made using

250 m bins and normalized by the total number of lidar profiles. It represents the frequency

(fraction) of finding a cloud layer base at a given height. The distribution in black is derived

from a laser ceilometer deployed at the BCO whose resolution corresponds to about 500 m. The

distribution from the CALIOP lidar in blue is determined over a 5x10◦ area just upstream of

Barbados at a 333 m footprint. We also show CALIOP distributions for the broader subtropics,

including all ocean between 15 and 30◦ in the Northern and Southern Hemisphere. These dis-

tributions illustrate that the cloud profile below 5 km is marked by two important height levels

where cloud layers tend to occur: near 700 m where cumuli have their base and near 1.5 - 2.5

km, where the inversion limits cumulus tops and stratiform layers can be found.



No.

Abbrev

iationM

odel

Modelin

gC

enter

L600hPa/900hPa

cloud

/con

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eme

1E

CW

MF

-LI

IFS

Lon

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urop

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entre

forM

ediu

m-

24/

3Tiedtke

[1993]/

Ran

geW

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Tiedtke

[1989]2

MP

IM-E

63M

PI-E

SM

-LR

Max

-Plan

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stitute

for11

/2

Tiedtke

[1989]/

EC

HA

M6.3

Meteorology

Sundqvist

etal.

[1989]3

MP

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62M

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SM

-LR

Max

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for11

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[1989]/

EC

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Sundqvist

etal.

[1989]4

BC

CB

CC

-CSM

1.1B

eijing

Clim

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7/

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al.[2010]

/Slin

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5C

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ESM

2C

anad

ianC

entre

forC

limate

14/

2von

Salzen

etal.

[2005]/

Modellin

gan

dA

naly

sis/M

cFarlan

eet

al.[2005]

6IP

SL

IPSL

-CM

5A-L

RIn

stitut

Pierre-S

imon

Lap

lace11

/1

Bon

yan

dEman

uel

[2001]/

Eman

uel

[1993]7

CN

RM

CN

RM

-CM

5C

entre

Nation

alde

Rech

erches

11/

2Gregory

andRow

ntree

[1990]/

Meteorologiq

ues

Ricard

andRoyer

[1993]8

MO

HC

Had

GE

M2-A

Met

Offi

ceH

adley

Cen

tre14

/2

Gregory

andRow

ntree

[1990]/

Lock

[2009]9

MR

IM

RI-C

GSM

3M

eteorologicalR

esearchIn

stitute

12/

1Yukim

otoet

al.[2012]

/Tiedtke

[1993]10

NC

AR

-C4

CA

M4

Nation

alC

enter

ofA

tmosp

heric

7/

1Rasch

andKristjan

sson[1998]

/R

esearchZhan

gan

dMcF

arlane

[1995]11

NC

AR

-C5

CA

M5

Nation

alC

enter

ofA

tmosp

heric

11/

2Gettelm

anet

al.[2010]

/R

esearchZhan

gan

dMcF

arlane

[1995]

Table

1.

List

ofm

odels

used

inth

ean

alysis,

inclu

din

gth

enum

ber

ofm

odel

levelsup

to600

hP

a(L

600hPa ),

and

betw

een

950-900hP

a(L

900hPa ),

and

references

toth

eirclou

dan

dcon

vectionsch

emes.

All

models

use

the

BO

ME

Xlo

cation,

excep

tth

e

EC

MW

F-L

I,M

PIM

-E63

and

MP

IM-E

62,w

hich

use

agrid

poin

tju

stupstream

ofB

arbad

os.A

llm

odels

have

outp

ut

every30

min

utes.

For

the

BC

Can

dN

CA

R-C

4m

odel

only

everysecon

dou

tput

stepis

used

inth

ean

alysis,

seesection

2.4.



Jan - Feb - MarSep - Oct - Nov

ILCLTLML

FT

Figure 2. Mean cloud and thermodynamic profiles are plotted, representative for the period

Jan - Mar (dry season) and Sep - Nov (wet season), from Barbados Cloud Observatory (BCO)

data and from model output for a location nearby Barbados (EMCWF-LI, MPIM-E63, MPIM-

E62) or the BOMEX location (all other models). Jan - Mar is depicted by solid lines, whereas

Sep - Nov is depicted by lighter-toned transparent lines. Variables shown from left to right:

cloud fraction (CF), the relative humidity (RH), the virtual potential temperature θv and the

frequency (fraction) of finding inversion layers at a given pressure level: pinv. Abbreviations for

the five layers that are identified in the BCO profiles refer to: ML = well-mixed layer, TL =

transition layer, CL = cloud (cumulus) layer, IL = inversion layer, FT = free troposphere.



Jan - Feb - Mar

Sep - Oct - Nov

a b c

d e f

Figure 3. A parameter that measures the shape of the profile of CF and CF at selected levels

are shown for the period Jan - Mar (top row) and Sep - Nov (bottom row). The three panels are

frequency distributions of: a,d) γ∗, which represents how bottom-heavy (large γ) or top-heavy

(small γ) the CF profile is, modified after Brient et al. (submitted to Climate Dynamics); b,e)

CFLCL(Table 2); and c,f) CFALOFT. For definitions see section 2.5 and 3.2. The observed CFLCL

and CFALOFT are shown in dashed black lines and the observed CCLCL and CCALOFT are shown

separately in solid black lines. All parameters are derived from daily mean profiles. The minor

tick marks indicate the binning that is used. In c-d and f-g the bin 0 - 0.1 excludes the frequency

of finding CF = 0, these are shown separately by the square markers at the left outset of each

panel.



Figure 4. The anomalies in thermodynamic and kinetic profiles for months with large values of

CFLCL (thick lines) and small values of CFLCL (thin lines). The anomalies are taken with respect

to a yearly running mean centered on each month. In the top row, the BCO data are shown,

whereby the lines correspond to the lower and upper quartile of ordered anomalies in CCLCL

instead of CFLCL. The following rows show the same, but for the models using CFLCL. We show

only those models in which the variance in monthly CFLCL is better explained by parameters

that represent the large-scale state than in observations (Table 3).



linea

r reg

ress

ion

coef

ficie

nt

Figure 5. The linear regression coefficient between CFLCL (models) or CCLCL (observa-

tions) with different parameters Xs determined on different time scales. The parameters include

〈RH〉ML, ∆CLRH, ∆ILRH, dθ/dzTL, ω825 and UL0, which are introduced in the text (section 4.1.2)

and the caption of Table 3). The time scales range from daily anomalies (from monthly means) to

monthly anomalies (from yearly means). The observations are denoted by black circles. Models

are denoted by squared markers, whose size is scaled by the amount of variance explained.



RHLCL

0 5 10 15 20 25 30time (days)

Figure 6. A sample time series of four-hourly CCLCL (observations) and CFLCL (models), as

well as RH near the LCL. Note that observed RH has a lower temporal resolution, because it is

available during nighttime only. Daytime values are simply constructed by interpolating between

nighttime values.



Abbreviation LCLσ2CFALOFT /σ2CFLCL

BCO 925 1.8ECMWF-LI 967 1.0MPIM-E63 941 0.2MPIM-E62 941 0.0BCC 945 1.3CCCma 911 0.03IPSL 978 0.2CNRM 904 0.5MOHC 930 0.8MRI 929 2.1NCAR-C4 930 1.0NCAR-C5 936 0.5

Table 2. The approximate level of cloud base or the LCL, taken as the level at which the

mean RH profile maximizes, restricted to levels with p > 850 hPa. Also tabulated is the ratio of

the variance in CFALOFT to CFLCL (for the models) and of the variance in CCALOFT to CCLCL

(for the observations).

a b

‘‘

Figure 7. Observed anomalous profiles of specific humidity q for 15 minute periods with large

values of cloudiness, denoted in black, and small values of cloudiness, denoted in grey. Cloudiness

is measured by CCLCL (a) and CCALOFT (b). The anomalies are taken with respect to the eight-

hourly nighttime mean q profile, of which the lower and upper quartiles are shown. Because the

observed temperature profiles only have an hourly resolution, temperature and therefore relative

humidity anomalies are not shown.



Abbreviation R2 (1d) Xs (1d) r2 (1d) Xm (1d) R2 (30d) Xs (30d) r2 (30d) Xm (30d)

BCO 0.24 ω825 0.10 〈RH〉ML 0.56 dθ/dzTL 0.30 UL0

ECMWF-LI 0.28 〈RH〉ML 0.21 〈RH〉ML 0.72 ω825 0.62 〈RH〉ML

MPIM-E63 0.28 〈RH〉ML 0.25 〈RH〉ML 0.62 〈RH〉ML 0.50 〈RH〉ML

MPIM-E62 0.66 〈RH〉ML 0.61 〈RH〉ML 0.80 〈RH〉ML 0.61 〈RH〉ML

BCC 0.56 〈RH〉ML 0.42 〈RH〉ML 0.72 dθ/dzTL 0.63 dθ/dzTL

CCCma 0.27 〈RH〉ML 0.13 〈RH〉ML 0.52 〈RH〉ML 0.31 〈RH〉ML

IPSL 0.02 - - - 0.12 - - -CNRM 0.44 dθ/dzTL 0.28 dθ/dzTL 0.67 dθ/dzTL 0.23 dθ/dzTL

MOHC 0.48 ω825 0.38 dθ/dzTL 0.83 dθ/dzTL 0.69 dθ/dzTL

MRI 0.30 ∆CLRH 0.15 dθ/dzTL 0.49 ∆CLRH 0.10 〈RH〉ML

NCAR-C4 0.66 dθ/dzTL 0.53 dθ/dzTL 0.75 dθ/dzTL 0.53 dθ/dzTL

NCAR-C5 0.50 〈RH〉ML 0.46 〈RH〉ML 0.67 〈RH〉ML 0.58 dθ/dzTL

Table 3. From left to right: the total fraction of variance in daily CFLCL (models) and CCLCL

(observations) explained using six parameters (see below); the parameter Xs that best explains

variance in daily CFLCL using a single regression; r2, the fraction of variance explained by Xs; the

parameter Xm that best explains variance in daily CFLCL using a multivariate regression (in which

other parameters are held constant). The following four columns show the same information for

monthly CFLCL. The parameters used are: 1) the average RH in the well-mixed layer 〈RH〉ML, 2)

the difference in RH across the cloud layer ∆CLRH, 3) the difference in RH across the inversion

layer ∆ILRH, 4) the θ lapse rate across the transition layer or mixed-layer top dθ/dzTL, 5) the

vertical velocity at 825hPa ω825 and 6) the near surface wind speed UL0.



q

Fb

q+δqηLCL

E

w

M

1. 2. 3.

Figure 8. Illustration of the negative feedback mechanism that constrains cloud amount near

cloud base, adapted from a Figure by Neggers et al. [2006]. In 1) a typical humidity profile above

the ocean’s surface is illustrated, along with the location of the top of the well-mixed layer η,

shown by a dashed line, the lifting condensation level(s), shown as a blue shaded layer, the surface

buoyancy flux Fb,s, and the processes that control the mass budget of the well-mixed layer (see

Equation 1): the mass flux M , the entrainment rate at η, E and the large-scale vertical velocity

at η, wη. In 2) a scenario is illustrated whereby the mixed-layer q is perturbed by adding an

amount of moisture δq. This lowers the surface energy input and the LCL, which in turn increases

cloud (core) fraction and through Equation 2 increases M . M removes moisture from the well-

mixed layer and transports it upwards, thereby deepening the layer, which leads to additional

downward mixing of drier free tropospheric air. In 3) the adjustment to a new equilibrium is

shown, whereby larger M has led to a lowering of η (through Equation 1), bringing it close again

to the LCL, thereby reducing cloud (core) fraction again.



Figure 9. The anomalous thermodynamic and kinetic profiles for months with large CCALOFT

(observations) or CFALOFT (models) (thick lines) and small values of CCALOFT,CFALOFT (thin

lines). The top row shows the observations, and the following rows those models that frequently

produce deeper cloud layers and for which large-scale parameters explain a larger fraction of

variance in cloudiness aloft than they do in observations (R2 (30d), Table 3).



Abbreviation R2 (1d) Xs (1d) r2 (1d) Xm (1d) R2 (30d) Xs (30d) r2 (30d) Xm (30d)

BCO 0.44 ∆CLRH 0.28 ∆CLRH 0.69 〈RH〉ML 0.42 ∆ILθECMWF-LI 0.39 ∆ILRH 0.24 ∆CLRH 0.79 ∆ILRH 0.48 UL0

MPIM-E63 0.19 ∆CLRH 0.15 ∆CLRH 0.46 ∆CLRH 0.16 ∆CLRHMPIM-E62 0.05 - - - 0.10 - - -BCC 0.54 ∆CLRH 0.31 ∆CLRH 0.76 ∆CLRH 0.49 ∆CLRHCCCma 0.11 - - - 0.47 ∆CLRH 0.32 ∆ILθIPSL 0.37 ∆ILRH 0.26 ∆CLRH 0.62 ∆ILRH 0.60 UL0

CNRM 0.45 ω825 0.35 〈RH〉ML 0.66 ω825 0.36 UL0

MOHC 0.52 ω825 0.43 ∆CLRH 0.72 ω825 0.36 ∆ILRHMRI 0.65 ω825 0.43 ∆CLRH 0.82 ∆CLRH 0.64 ∆CLRHNCAR-C4 0.58 ∆CLRH 0.29 ∆CLRH 0.80 ∆ILRH 0.48 ∆CLRHNCAR-C5 0.49 ∆CLRH 0.28 ∆CLRH 0.67 ∆CLRH 0.50 ∆CLRH

Table 4. Similar to Table 3, but then for the variance explained in CCALOFT (observations)

and CFALOFT (models). The set of parameters used is the same, with one main difference,

dθ/dz = ∆ILθ. For the observations and those models that produce clouds beyond 1 km often,

the relationship of CCALOFT,CFALOFT with dθ/dzTL is similar to that of CCLCL,CFLCL with

dθ/dzTL.

linea

r reg

ress

ion

coef

ficie

nt

Figure 10. As in Figure 5, but then for the variance explained in CFALOFT (models) and

CCALOFT (observations). The set of parameters used is the same with one main difference, ∆ILθ

is used instead of dθ/dzTL.



a b c

d e f

g

Figure 11. Each panel displays the difference (δ) in a parameter between days with a uniform

distribution of moisture across the cloud layer and days with a less uniform distribution of

moisture, as measured by ∆CLRH = RH850-RHLCL. δ is derived as follows: days are ordered

by ∆CLRH from high to low values. The difference between the upper and lower quartiles of

days are taken: δ ≡ φupper − φlower, whereby φupper and φlower are the average φ’s over the upper

respectively lower quartile of days. The selected parameters are: (a - g) CFALOFT, CFLCL, γ∗

(changes in the shape of the cloud profile, section 3.2), 〈RH〉ML, ∆ILθ, dθ/dzTL and ∆ILRH =

RH700 - RH850. The grey shaded box indicates negative δ’s.



Fq

inversion

Fq

inversion

a

b

a

c

Figure 12. An illustration of different model behaviour for a more uniform distribution of

moisture across the cloud layer measured by ∆CLRH (see also Figure 11). In this illustration

we imagine an increase in surface moisture flux (Fq) to trigger an increase in vertical moisture

transport towards the upper cloud layer. Days are ordered by ∆CLRH from high to low values.

The modeled CF and RH profiles are averaged over the upper and lower quartiles of days and

shown in dark respectively light solid lines. The BCO observations are shown as a reference at

the top. The MPIM-E62 model is an example of a model that effectively reduces CFLCL when

moisture is mixed upward over a deep layer, whereby gradients and the inversion diminish. The

MOHC model is an example of a model that increases CFLCL along with CFALOFT as moisture

is mixed upward, whereby the structure of the trade-wind layer and the inversion is maintained.


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